A hybrid quark-nucleon model of nuclei is developed in which nucleons merge into multiquark bags at short distances. This model is applied to calculate mass differences between /sup 3/He and /sup 3/H and a number of other mirror nuclei. For light nuclei we obtain a reduction of the discrepancy between experiment and conventional theory. Probabilities for the formation of six-quark bags and nine-quark bags in these nuclei are evaluated, and the consequences of our results are discussed. In particular we comment on the compatibility of conventional and the hybrid quark-nucleon results.